Unbounded asymptotic equivalences of operator nets with applications
Positivity, vol.23, no.4, pp.829-851, 2019 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 23 Issue: 4
- Publication Date: 2019
- Doi Number: 10.1007/s11117-018-0640-z
- Journal Name: Positivity
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.829-851
- Keywords: Unbounded convergence, Asymptotic equivalence, Operator nets
- TED University Affiliated: No
Abstract
Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and d on a vector lattice, we study d-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on d-martingale and d-Lotz–Räbiger nets.